1. Field of the Invention
The present invention relates to carbon capture and storage (CCS), and particularly to a method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs based on measuring electrical conductivity and seismic P-wave velocity of a cap rock above a carbon dioxide storage reservoir.
2. Description of the Related Art
Carbon capture and storage (CCS) (sometimes also referred to as carbon capture and sequestration) is the process of capturing waste carbon dioxide (CO2) from large point sources (such as fossil fuel power plants), transporting it to a storage site, and depositing it where it will not enter the atmosphere. The waste CO2 is typically stored in an underground geological formation. The aim of CCS is to prevent the release of large quantities of CO2 into the atmosphere from fossil fuel use in power generation and other industries. CCS is a potential means of mitigating the contribution of fossil fuel emissions to global warming and ocean acidification. Although CO2 has been injected into geological formations for several decades for various purposes, including enhanced oil recovery, the long term storage of CO2 is a relatively new concept.
One of the most important aspects associated with carbon capture and storage is the ability to detect CO2 leakage from the storage reservoir at an early stage. Seismic and electromagnetic (EM) methods can be used to detect changes in physical properties, such as porosity and fluid saturation of the subsurface layers due to CO2 leakage. With regard to EM methods, the electrical conductivity (σ) is sensitive to resistive gaseous or supercritical CO2 replacing a conductive pore fluid in a porous medium. Thus, electromagnetic surveying can be a significant complementary technique to seismic monitoring. While seismic methods can be used to detect gas with limited quantitative information, electromagnetic methods are robust when it comes to predicting gas saturation.
Seismic measurements can provide information about the elastic properties of the storage medium, such as P-wave velocity (VP), while EM measurements can provide information about the EM properties (namely, electrical conductivity) of the subsurface layers. As CO2 migrates out of the reservoir, the conductivity and the P-wave velocity of the new host rock will change. The integration of rock properties from seismic and EM data can provide better delineation of the leakage pathway than the physical properties from each method individually. Thus, it would obviously be desirable to provide a technique for the joint inversion of porosity and water saturation from electrical conductivity (σ) and P-wave velocity (VP) measurements.
The electrical properties of rocks depend on the pore geometry, the constituent minerals, the type of fluids and their saturations. Hydrocarbons and CO2 are considered to be electrically resistive. The electrical resistivity of reservoir rocks is highly sensitive to changes in water saturation. This high sensitivity to water saturation in a reservoir can be exploited by EM techniques, where the response is a function of the rock bulk electrical resistivity.
Archie's law is an empirical relation which is used to describe the electrical resistivity of sedimentary rocks (ρt) (Ω·m) as a function of water saturation, porosity and pore-fluid resistivity (ρw) as:ρt=aφ−mSw−nρw,  (1)where m is the cementation factor (between 1.8 and 2.0 for sandstones), n is the saturation exponent (typically around 2), a is the tortuosity factor, φ is the porosity and Sw is the water saturation. The formation factor, F, is defined as:
                    F        =                              a                          ϕ              m                                =                                    ρ                              0                ⁢                                                                                                      ρ              w                                                          (        2        )            where ρ0 is the resistivity of the rock filled with only water (Sw=1). The ratio between ρt and ρ0 is known as the resistivity index, I, thus:
                    I        =                                            ρ              t                                      ρ              0                                .                                    (        3        )            In terms of conductivity (S/m), Archie's law can be written as:σ=(1−φ)pσs+σfφm,  (4)where σf is the conductivity of the fluid filling the pore and σs is the conductivity of the solid minerals. Each phase has its own connectivity and a representative exponent (m and p). Large exponents occur for low connectivity phases, and small exponents occur for high connectivity phases. The exponent p is given by:
                    p        =                                            log              ⁡                              (                                  1                  -                                      ϕ                    m                                                  )                                                    log              ⁡                              (                                  1                  -                  ϕ                                )                                              .                                    (        5        )            
The Hermance model is modification of Archie's law that has been developed to study the electrical conductivity of the crust and mantle. The relationship relates the bulk rock resistivity to the pore fluid resistivity and porosity as:σ=(σf−σs)Øm+σs=(1−φm)σs+σfφm.  (6)If σs→0, then equation (6) reduces to Archie's law.
The porosity of two-constituent composite rock in terms of the lower and upper Hashin-Shtrikman (HS) bounds on the electrical conductivity is given as:
                              ∅                      -            HS                          =                              (                                                            σ                  s                                -                                  σ                  HS                  -                                                                              σ                  s                                -                                  σ                  f                                                      )                    -                      (                                                            σ                  f                                +                                  2                  ⁢                                      σ                    s                                                                                                σ                  HS                  -                                +                                  2                  ⁢                                      σ                    s                                                                        )                                              (        7        )                                                      ∅                          +              HS                                =                                    (                                                                    σ                    s                                    -                                      σ                    HS                    +                                                                                        σ                    s                                    -                                      σ                    f                                                              )                        -                          (                                                3                  ⁢                                      σ                    f                                                                                        σ                    HS                    +                                    +                                      2                    ⁢                                          σ                      s                                                                                  )                                      ,                            (        8        )            where σHS− and σHS+ are the lower and upper Hashin-Shtrikman bounds for electrical conductivity, respectively.
A self-similar theory has been developed to study the dielectric response of water-saturated rocks based on a realistic model of the pore space. In order to include the local environmental effects around a grain, a self-similar model is generated by envisioning that each rock grain itself is coated with a skin made of other coated spheres. In the self-similar model, the conductivity of the rock satisfies:
                              ϕ          =                                    ∑                              i                =                0                            N                        ⁢                                          p                i                            ⁡                              (                                                      σ                    -                                          σ                      i                                                                                                  2                      ⁢                      σ                                        -                                          σ                      i                                                                      )                                                    ,                            (        9        )            where σi and pi are the conductivity and the volume fraction of the i-th phase, respectively. A water-wet rock that remains percolating for small values of porosity can be obtained from the assumption that water is the starting host material into which infinitesimal amounts of spheres of matrix and fluids are gradually included. This model is in agreement with Archie's law because it preserves the continuity of the water phase. For two constituents (solid and fluid), the solution is given as:
                              ϕ          =                                    f              ⁡                              (                                  σ                  ,                                      σ                    s                                    ,                                      σ                    f                                                  )                                      =                                          (                                                                            σ                      s                                        -                    σ                                                                              σ                      s                                        -                                          σ                      f                                                                      )                            ⁢                                                (                                                            σ                      f                                        σ                                    )                                W                                                    ,                            (        10        )            where W=⅓ for spherical inclusions. The EM properties of finely plane-layered media can be obtained by using Backus averaging. Considering a plane-layered medium where each layer is homogeneous, isotropic and thin (compared to the wavelength of the electromagnetic wave), then, if the layers interfaces are parallel to the x-y plane, the properties are independent in the x and y directions. The equivalent medium is transversely isotropic and can be described with two components of the conductivity tensor:
                                          (                                                                                σ                    11                                                                                                                    σ                    33                                          -                      1                                                                                            )                    =                                    (                                                                                          σ                      1                                                                                                  σ                      2                                                                                                                                  σ                      1                                              -                        1                                                                                                                        σ                      2                                              -                        1                                                                                                        )                        ⁢                          (                                                                                          p                      1                                                                                                                                  p                      2                                                                                  )                                      ,                            (        11        )            where it is assumed that there are two thin layers of proportions p1 and p2 and conductivities σ1 and σ2. The proportions p1 and p2 can be expressed as:
                                          p            1                    =                                                                      σ                  11                                -                                  σ                  2                                                                              σ                  1                                -                                  σ                  2                                                      =                                                            σ                  11                                      -                    1                                                  -                                  σ                  2                                      -                    1                                                                                                σ                  1                                      -                    1                                                  -                                  σ                  2                                      -                    1                                                                                      ⁢                                  ⁢        and        ⁢                                  ⁢                              p            2                    =                      1            -                                          p                1                            .                                                          (        12        )            
A formulation that is commonly used to estimate the electromagnetic properties of rocks is known as the complex refractive index method (CRIM). For negligible dielectric permittivity, the CRIM model can be expressed as:σ=[(1−φ)·Σi=1Nsolidfi,(σi)1/2+φ·(Swσw1/2+Soσo1/2+Sgσg1/2)]2,   (13)where fi is the fractional volume of the i-th solid component; σi, σw, σo, and σg are the conductivity of the i-th solid phase, water, oil and gas, respectively; and Sw, So, and Sg are the saturations of water, oil, and gas, respectively. The CRIM model has been found to give good results at high frequencies (above ˜0.5 GHz). The CRIM model has also been used for electromagnetic data at low frequencies (˜200 Hz) to obtain electrical conductivity. The electrical conductivity as a function of saturation, porosity and clay content based on the CRIM model is given by:σ=[(1−φ)·Cσc1/2+φ(1−Sg)σb1/2]2,  (14)where C is the clay content, σc, and σb are the clay and brine conductivities, respectively, and Sg is the gas saturation, FIGS. 2A and 2B show that the CRIM conductivity-porosity model fits the shale and sandy sections of a well in the Gullfaks field of the North Sea, respectively, better than other models.
The CRIM equation is commonly expressed by the following formula:√{square root over (σ)}=(1−φ)√{square root over (σm)}+φSw√{square root over (σw)}+φ(1−Sw)√{square root over (σa)},  (15)where σm, σw, and σa are the electrical conductivities of the solid matrix, water, and air in the material, respectively. For a rock with a multi-mineral matrix and/or multi-phase fluid, the CRIM model of equation (13) can be used. σw is typically calculated as:σw=0.15×TDS,  (16)where TDS indicates the total dissolved solids in parts per thousand (ppt) or g/L. FIG. 3 shows a plot of σ in equation (15) as a function of φ and Sw in a typical brine saturated shale. Table 1 lists typical values of rock and fluid properties used to generate plots of the electrical conductivity and P-wave velocity, including the plot of FIG. 3. These values are representative of shales.
TABLE 1Rock and Fluid Properties for Typical Brine-Saturated ShaleRock/fluid propertyValueUnitsQuartz volume (νq)0.3FractionClay volume (νc)1 − νq = 0.7FractionRock porosity (φ)0.1FractionRock water saturation (Sw)1.0FractionConductivity of air (σa)0Siemen/meter (S/m)Conductivity of water (σw)Equation (13)S/mConductivity of oil (σo)0.0001S/mConductivity of quartz (σq)0.001S/mConductivity of clay (σc)0.01S/mBulk modulus of quartz (Kq)39Gigapascal (GPa)Bulk modulus of clay (Kc)20GPaBulk modulus of air (Ka)1.01 × 105PaBulk modulus of water (Kw)2.25GPaShear modulus of quartz (Gq)40GPaShear modulus of clay (Gc)15GPaDensity of air (ρa)1kg/m3Density of water (ρw)1000kg/m3Density of quartz (ρq)2650kg/m3Density of clay (ρc)2500kg/m3Shale critical porosity (φc)0.4Fraction
Thus, a method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs solving the aforementioned problems is desired.